Find out from the websites that the purchases have been made, what the address they are going to are? I'd like nothing more that to be able to show up when the stuff they are buying illegally show up at their door with the police.

You shouldn't chase the crook and put yourself in danger. Call the credit card company and have them deal with those fraudulent charges.

That's pretty much the reason why the website most likely won't reveal the information to you. The police will do fine without you there. Just report the theft to your credit card company and file a dispute on the charge as soon as possible, then report the theft to the police.

call the credit card company
report the illegal use.and dispute it.
get a new card.

Don't waste time on answers call your credit company and report this.

[Hedwig]

Exactly. First, report the theft to the credit card company. Normally, you have no liability for illegal use of the card. However, if you know about it and don't report it, you may lose that protection and you may become liable for charges made by the thief.

You second call (immediately following the first one) should be to the police. Insist that they take a report of identity theft, even if they balk. Get a copy of that police report. It will come in handy later.

Your third call should be to one of the three credit reporting agencies to place a fraud alert on your file. Calling one will place the alert on all three.